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East Anglia Tea Company

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Question;East Anglia Tea Company;The East Anglia Tea Company imports three varieties of tea;from Asia: black tea, oolong tea, and green tea. The company purchases 70;pounds of black tea every week, at a cost of $2.70 per pound. Also, it;purchases 120 pounds of oolong tea at $3.00 per pound, and 150 pounds of green;tea at $2.10 per pound, every week. By mixing these teas in various;combinations, the company creates three tea blends, Mongolian, Manchu, and;House, that it sells to a packaging company for further processing. Mongolian;blend is at least 70% black tea but no more than 10% green tea. Manchu blend is;at least 30% black tea and at least 40% oolong tea. The company?s House blend;is no more than 60% green tea, but its oolong tea component must be at least;30%. The wholesale prices per pound that East Anglia charges the packaging;company are $6.50 for Mongolian blend, $7.25 for Manchu blend, and $6.00 for;House blend.;(a.) How;much of each blend should the East Anglia Tea Company make each week to;maximize its profit? Create a linear programming model, and solve it using the;Solver utility of Excel.;(b.)Discuss;the sensitivity ranges of the decision variables. Point out and explain any;interesting facts about those ranges.;(c.) Discuss;the sensitivity ranges that pertain to the total amounts (of the three tea;varieties) purchased each week. How would variations in those amounts affect;the optimal product mix? What do the shadow prices imply about the relative;values of the three resources (teas)?;Assignment 1. Linear Programming Case Study;Your instructor will assign a linear programming project for;this assignment according to the following specifications.;It will be a problem with at least three (3) constraints and at;least two (2) decision variables. The problem will be bounded and feasible. It;will also have a single optimum solution (in other words, it won?t have;alternate optimal solutions). The problem will also include a component that;involves sensitivity analysis and the use of the shadow price.;You will be turning in two (2) deliverables, a short writeup of;the project and the spreadsheet showing your work.;Writeup.;Your writeup should introduce your solution to the project by;describing the problem. Correctly identify what type of problem this is. For;example, you should note if the problem is a maximization or minimization;problem, as well as identify the resources that constrain the solution. Identify;each variable and explain the criteria involved in setting up the model. This;should be encapsulated in one (1) or two (2) succinct paragraphs.;After the introductory paragraph, write out the L.P. model for;the problem. Include the objective function and all constraints, including any;non-negativity constraints. Then, you should present the optimal solution;based on your work in Excel. Explain what the results mean.;Finally, write a paragraph addressing the part of the problem;pertaining to sensitivity analysis and shadow price.;Excel.;As previously noted, please set up your problem in Excel and;find the solution using Solver. Clearly label the cells in your spreadsheet.;You will turn in the entire spreadsheet, showing the setup of the model, and the;results.

 

Paper#60293 | Written in 18-Jul-2015

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